Question

Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring, with spring constant k� = 95.0 N/mN/m , is compressed 5.00 mm from its equilibrium position, and a glass sits 19.8 mm from her outstretched foot.

Assuming that Albertine's mass is 60.0 kgkg , for what value of μk�k, the coefficient of kinetic friction between the chair and the waxed floor, does she just reach the glass without knocking it over? Use g� = 9.80 m/s2m/s2 for the magnitude of the acceleration due to gravity.

Answer 1

To calculate the coefficient of kinetic friction, we can use Hooke's law to determine the force exerted by the compressed spring and the weight of the object to find the force of friction. Equating the force of friction to the force exerted by the spring allows us to solve for the coefficient of kinetic friction, which is approximately 0.0008.

Step-by-step explanation:

To calculate the coefficient of kinetic friction, we need to consider the forces acting on Albertine. The force exerted by the compressed spring is given by Hooke's law: F = k*x, where F is the force, k is the spring constant, and x is the displacement of the spring from its equilibrium position. In this case, the force exerted by the spring is F = 95.0 N/m * 0.005 m = 0.475 N.

The force of friction is equal to the coefficient of kinetic friction multiplied by the normal force. The normal force is equal to the weight of Albertine, which is given by her mass multiplied by the acceleration due to gravity: N = 60.0 kg * 9.80 m/s² = 588 N. Therefore, the force of friction is Ff = μk * N = μk * 588 N.

Since we want to find the value of μk that allows Albertine to just reach the glass without knocking it over, the force of friction must be equal to the force exerted by the compressed spring: Ff = 0.475 N. Therefore, we can set up the equation: μk * 588 N = 0.475 N. Solving for μk, we find: μk = 0.475 N / 588 N = 0.0008 (rounded to four decimal places).